Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A) = 0.5, P(B) = 0.2, and P(A n B) = 0.05. (a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event AU B). (b) What is the probability that the selected individual has neither type of card? (c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard. O A'UB' O An B' O AUB' O A'n B' O A'n B Calculate the probability of this event.
Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A) = 0.5, P(B) = 0.2, and P(A n B) = 0.05. (a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event AU B). (b) What is the probability that the selected individual has neither type of card? (c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard. O A'UB' O An B' O AUB' O A'n B' O A'n B Calculate the probability of this event.
A First Course in Probability (10th Edition)
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Transcribed Image Text:Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard. Suppose that P(A) = 0.5, P(B) = 0.2, and P(A n B) =
0.05.
(a) Compute the probability that the selected individual has at least one of the two types of cards (i.e., the probability of the event A U B).
(b) What is the probability that the selected individual has neither type of card?
(c) Describe, in terms of A and B, the event that the selected student has a Visa card but not a MasterCard.
O A'U B'
O An B'
O AU B'
Ο Α' n '
O A'n B
Calculate the probability of this event.
Expert Solution
Step 1
Given that
P(A)= 0.5 , P(B)=0.2
And P(A ∩ B )= 0.05
Formula used
P( A U B)= P(A) + P(B) - P(A ∩ B )
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Solved in 4 steps
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